//    PG (470)

u1 = [1/2,sqrt(3)/2]
u2 = [-sqrt(3)/2,1/2]

//    For a given vector x = (x1,x2), it can be written as
//                    x = alpha1*u1 + alpha2*u2
//    alpha1 = (x1+x2*sqrt(3))/2
//    alpha2 = (x2-x1*sqrt(3))/2

//    (1,0) = (1/2)*u1 - (sqrt(3)/2)*u2